Your seat is actually three different systems. First you have the support system, which is the mounting frame, shell, seat pan, etc. Then you have the padding. Last, you have the harness, which is the part that you need to replace (don't bother trying to make it work).
Call your nearest skydiving center, and ask for the phone number of someone who does custom harnesses. Take the seat and son to them and ask them to make a custom wearable harness made which you will put on outside the plane, set His Lordship into the seat, then attach the harness to the seat to secure him in place. Attachment might be with seatbelt buckles, Frost clips, etc., connecting to the "seat side" of the harness, which is held in place by pin/cone/grommet closures and either a D-ring or a Little Red Apple to release everything instantly.
The advantages of this are that you can adjust the size to fit over whatever clothing he wears or as he grows, and the harness makes a really good handle to pull him out of the plane if you're in a hurry (without dislocating his shoulder). It also means that you can replace the seat pan if a better one comes along. When he gets bigger, you can upgrade the system with inertia recoil attached to the regular seat with a booster seat for support.
It will cost you more money but will be worth it.